ROCHESTER, Mich. — Republican presidential hopefuls agreed Wednesday night that Europe's countries should rise or fall on their own without any American bailout and warned that failing to cut budget deficits at home will doom the U.S. economy to the same sort of crisis that now plagues Greece and Italy.

Though sexual harassment allegations facing Herman Cain have dominated news coverage of the Republican campaign for more than a week, the debate focused almost entirely on economic worries and proposed solutions.

"Europe is able to take care of their own problems. We don't want to step in and bail out their banks and their economies," former Massachusetts Gov. Mitt Romney said as he and GOP rivals met for the first time in three weeks in campaign debate.

Even so, he said the United States should continue contributing to organizations like the International Monetary Fund that are working to prevent a meltdown in troubled economies overseas.,

Rep. Ron Paul of Texas was more emphatic about Europe's debt. "You have to let it liquidate. We took 40 years to build up this worldwide debt," he added.

Cain said there wasn't much the United States could do to directly to help Italy at present because the economy there is in such difficult shape. "We need to focus on the economy or we will fail," he said, referring to the U.S. and calling for spending cuts, a strong dollar and measures to stimulate growth.

The Cain accusations did come up, though briefly.

The debate marked the first time the Republican rivals had gathered since complaints emerged from several women accusing Cain of sexual harassment, allegations that the unlikely front-runner in the polls has strongly denied.

"The American people deserve better than someone being tried in the court of public opinion due to unfounded accusations," he said when the question came up early in the debate. "I value my character and my integrity more than anything else. And for every one person that comes forward with an unfair accusation there are probably, there are thousands who come forward and say none of that ever happened with Herman Cain."

Romney, a former venture capitalist, was asked if he would keep Cain on the job as a CEO given the accusations. He responded, "Herman Cain is the person to respond to these questions. He just did."

The announced topic for the evening was the economy, a subject that produced few if any early sparks among rivals who often spar energetically.